Kernels for products of L-functions

Abstract

The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properties of these series and their non-holomorphic analogs and show their connection to values of L-functions outside the critical strip.

27 pages. In version 3: a formula in section 7 is corrected and the theorem in section 2.3 is stated more clearly. Further small improvements

References in corpus (1)

• Hecke operators on period functions for ${\Gamma }_0(n)$

Cited by in corpus (3)

• Rankin-Cohen brackets and Serre derivatives as Poincaré series
• Kernels for products of Hilbert L-functions
• Simultaneous nonvanishing of the Products of L-functions associated to elliptic cusp forms